Question

the tires of a bicycle have radius 12.0 in. and are turning at the rate of 205 revolutions per min. see the figure. how fast is the bicycle traveling in miles per hour? (hint: 5280 ft = 1 mi)
given that the tires are on the ground, how fast is the bicycle traveling?
mph (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate the circumference of the tire

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 12.0$ in, so $C=2\pi\times12 = 24\pi$ in.

Step2: Find the distance traveled per minute

The tire makes 205 revolutions per minute. The distance $d$ traveled per minute is the number of revolutions times the circumference. So $d = 205\times24\pi$ in/min.
$d=205\times24\pi=4920\pi$ in/min.

Step3: Convert inches per minute to feet per minute

Since 1 foot = 12 inches, the distance in feet per minute is $\frac{4920\pi}{12}=410\pi$ ft/min.

Step4: Convert feet per minute to miles per hour

There are 5280 feet in a mile and 60 minutes in an hour.
The speed $v$ in miles per hour is $v=\frac{410\pi\times60}{5280}$ mph.
$v=\frac{24600\pi}{5280}=\frac{410\pi}{88}\approx\frac{410\times 3.14159}{88}\approx14.6$ mph.

Answer:

$14.6$